LEARNATHON

III

Competition for grade 6 to 10 students! Learn, solve tests and earn prizes!

Learn more### Theory:

Length is one of the fundamental quantity that cannot be conveyed in any other way. Other measurements, in derived quantities such as area and volume, can be calculated using length.

Area is the amount of space on a flat or a plane surface or a two-dimensional object. In general, length is a fundamental quantity. Here, length is

**multiplied twice**to calculate the area, which is a derived quantity.The formula is given as,

**$\begin{array}{l}\mathit{Area}=\mathit{Length}\times \mathit{Breadth}\\ =l\times b\end{array}$**

Using the above formula, one can find the area of a book or a house or even a plot of land.

Unit of area \(=\) \({metre} \times{metre}\) \(=\) \(metre^2\) (or) \(m^2\)

The SI unit of the area of a surface is \(square\ metre\) (\(m^2\)) since it is a product of two lengths.

One square metre denotes the area enclosed inside a square of side \(1\ metre\).

Even though the area is measured in a \(square\ metre\), the surface does not have to be square.

Area of regular figures

Some of the formulae used to find the area of regularly shaped figures is shown below.

Shape | Two-dimensional figure | Area |

Square | $\begin{array}{l}\mathit{side}\times \mathit{side}\\ a\times a={a}^{2}\end{array}$ | |

Rectangle | $\begin{array}{l}\mathit{length}\times \mathit{breadth}\\ l\times b\end{array}$ | |

Circle | $\begin{array}{l}\mathrm{\pi}\times {\mathit{radius}}^{2}\\ \mathrm{\pi}{r}^{2}\end{array}$ | |

Triangle | $\begin{array}{l}\frac{1}{2}\times \mathit{base}\times \mathit{height}\\ \frac{1}{2}\times b\times h\end{array}$ |